A modular invariance property of multivariable trace functions for regular vertex operator algebras

Krauel, Matthew; Miyamoto, Masahiko

doi:10.1016/j.jalgebra.2015.07.013

Cited by 28 publications

(23 citation statements)

References 10 publications

(24 reference statements)

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“…(2) This follows immediately from Theorem 2 of [28]. We are now ready to prove the main result in this section.…”

Section: Global Dimensions and Quantum Dimensions Of Some Diagonal Comentioning

confidence: 73%

Quantum dimensions and irreducible modules of some diagonal coset vertex operator algebras

Lin

2020

Lett Math Phys

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In this paper, under the assumption that the diagonal coset vertex operator algebra C(L g (k + l, 0), L g (k, 0) ⊗ L g (l, 0)) is rational and C 2 -cofinite, the global dimension of C(L g (k + l, 0), L g (k, 0) ⊗ L g (l, 0)) is obtained, the quantum dimensions of multiplicity spaces viewed as C(L g (k + l, 0), L g (k, 0) ⊗ L g (l, 0))-modules are also obtained. As an application, a method to classify irreducible modules of C(L g (k + l, 0), L g (k, 0) ⊗ L g (l, 0)) is provided. As an example, we prove that the diagonal coset vertex operator algebra C(L E8 (k + 2, 0), L E8 (k, 0) ⊗ L E8 (2, 0)) is rational, C 2 -cofinite, and classify irreducible modules of C(L E8 (k + 2, 0), L E8 (k, 0) ⊗ L E8 (2, 0)).

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“…(2) This follows immediately from Theorem 2 of [28]. We are now ready to prove the main result in this section.…”

Section: Global Dimensions and Quantum Dimensions Of Some Diagonal Comentioning

confidence: 73%

Quantum dimensions and irreducible modules of some diagonal coset vertex operator algebras

Lin

2020

Lett Math Phys

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“…Theorem 2.4 ( [28,68]). Let W be a rational C 2 -cofinite vertex operator algebra and suppose that ω = ω ′ + ω ′′ where ω is the conformal vector of W , and ω ′ and ω ′′ generate commuting representations of the Virasoro algebra.…”

Section: Modularitymentioning

confidence: 99%

Self-dual vertex operator superalgebras and superconformal field theory

Creutzig

Duncan

Riedler

2017

J. Phys. A: Math. Theor.

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Recent work has related the equivariant elliptic genera of sigma models with K3 surface target to a vertex operator superalgebra that realizes moonshine for Conway's group. Motivated by this we consider conditions under which a self-dual vertex operator superalgebra may be identified with the bulk Hilbert space of a superconformal field theory. After presenting a classification result for self-dual vertex operator superalgebras with central charge up to 12 we describe several examples of close relationships with bulk superconformal field theories, including those arising from sigma models for tori and K3 surfaces.

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“…Since U is strongly rational and V is positive-energy C 2 -cofinite, the two-variable trace function converges absolutely to a holomorphic function on H×H for all u ∈ U , v ∈ V , and simple A-modules X. Then the hypotheses of [KM,Theorem 1] are satisfied, and we conclude…”

Section: Applicationsmentioning

confidence: 78%

On rationality for $C_2$-cofinite vertex operator algebras

McRae¹

2021

Preprint

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Let V be an N-graded, simple, self-contragredient, C2-cofinite vertex operator algebra. We show that if the S-transformation of the character of V is a linear combination of characters of V -modules, then the category C of grading-restricted generalized V -modules is a rigid tensor category. We further show, without any assumption on the character of V but assuming that C is rigid, that C is a factorizable finite ribbon category, that is, a not-necessarily-semisimple modular tensor category. As a consequence, we show that if the Zhu algebra of V is semisimple, then C is semisimple and thus V is rational. The proofs of these theorems use techniques and results from tensor categories together with the method of Moore-Seiberg and Huang for deriving identities of two-point genus-one correlation functions associated to V .We give two main applications. First, we prove the conjecture of Kac-Wakimoto and Arakawa that C2-cofinite affine W -algebras obtained via quantum Drinfeld-Sokolov reduction of admissible-level affine vertex algebras are strongly rational. The proof uses the recent result of Arakawa and van Ekeren that such W -algebras have semisimple (Ramond twisted) Zhu algebras. Second, we use our rigidity results to reduce the "coset rationality problem" to the problem of C2-cofiniteness for the coset. That is, given a vertex operator algebra inclusion U ⊗ V ֒→ A with A, U strongly rational and U , V a pair of mutual commutant subalgebras in A, we show that V is also strongly rational provided it is C2-cofinite. ROBERT MCRAE 6. Applications 61 6.1. Rationality for C 2 -cofinite W -algebras 61 6.2. Rationality for C 2 -cofinite cosets 66 Appendix A. Differential equations 69 Appendix B. The assumption in Theorem 6.4 for odd nilpotent orbits 74 B.1. Classical types 74 B.2. Exceptional types 76 References 82

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A modular invariance property of multivariable trace functions for regular vertex operator algebras

Cited by 28 publications

References 10 publications

Quantum dimensions and irreducible modules of some diagonal coset vertex operator algebras

Quantum dimensions and irreducible modules of some diagonal coset vertex operator algebras

Self-dual vertex operator superalgebras and superconformal field theory

On rationality for $C_2$-cofinite vertex operator algebras

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